3 Forward Prices-Determination

8/10/2019 3 Forward Prices-Determination

1/26

BGDF (201315) 12

Dr. Pankaj Varshney

D F /F

D F / F 2

. C

* *

P(1+ ) = P

/

= ( 1)

= (1+ )

ln

F C M :

F M C :


2/26

BGDF (201315) 12

Dr. Pankaj Varshney

C= 12% (); =4

D F / F 3

. C

/ 0.12/4

= ( 1) = 4( 1) = 4(1.03045 1)

I 4% , ?

= 4% ; = 2;

0.04 = 2 (1+ ) = 2(0.019803) = 0.039606 = 3.96% ()

2ln

I 12% ,

?

= 4(0.03045) = 0.12182 = 12.18%

D F / F 4

. C

I 10% ,

?

2= 10% ; 4= ? * * P(1+ ) = P(1+ )

2/42

4

= 4 (1+ ) 12

2/4

4

0.10 = 4 (1+ ) 1 0.9878 9.878%

2

= =

/

= (1+ ) 1


3/26

BGDF (201315) 12

Dr. Pankaj Varshney

D F / F 5

D F/F

: A I .

E..: S, , G , S .

C : A

.

E..: O, .

D F / F 6

D F/F

A:

N .

U .

A

.

M

.


4/26

BGDF (201315) 12

Dr. Pankaj Varshney

D F / F 7

D F/F

( , B)

( , D , C

)

( , )

D F / F 8

S

R. 500/(S0) I () 5% .

C 3 F (F0) R. 535/.

A ,

:

:

) B R. 500/ 3 @ 5% .

) B R.500/ C M

) S 3 F0

R. 535/.


5/26

BGDF (201315) 12

Dr. Pankaj Varshney

D F / F 9

A 3 :T :

) R I

= R. 500/ + I @ 5% 3

= 500*(0.05*3/12) = 500*1.0126= R. 506/ (.)

) D F

R. 535/ .

C F: : 535/ : . 506/

B ,

R.29/ .. (535506)

D F / F 10

N , 3 (F0 ) R. 475/

( R. 535/)

A

:

:

) S S @ R. 500/ ,

) I 3 @ =5%.., ) B 3 @ R. 475/


6/26

BGDF (201315) 12

Dr. Pankaj Varshney

D F / F 11

A 3:T :

) R R. 500/ 3

= 500* (0.05)*(3/12) = R. 506/

) R

R 475/ .

C F: : 506/ : . 475/

B ,

R.31/ .. (506 475)

D F / F 12

F = 535/ F = 475/

A = 0

B (R. 500/ @ 5%

3 )

B

S 3 F C @

R. 535/.

B 3 F @

R. 475/

S

I @ 5% 3

.

A = 3

R

D F

R. 535/.

R

R

F & R. 475/

R .

= . 29/ = 31/

C A C A


7/26

BGDF (201315) 12

Dr. Pankaj Varshney

D F / F 13

T, NOT R. 506/

.

F NO ABITRAGE , F P (F0)

R. 506/.

F0 = 0

= 500(0.05)3/12 = 500*1.0126 = . 506/

F (F0) = 0

D F / F 14

A 6

. 2800/.

8%. 6

?

S0= 2,800/ ; = 8% ; T = 6/12 = 0.5

F P (F0) = S0T

= 28000.08*0.5 = 2800*1.04081

= .2,914.27


8/26

BGDF (201315) 12

Dr. Pankaj Varshney

D F / F 15

C 85/ 3

. 90/. 6%

. () 3

, ?

S0= 85/ ; = 6% ; T = 3/12 = 0.25 ; F0=R.90/

T F P (FT0)=S0T

=850.06*0.25= R. 86.28 < R. 90/

A CC::

B R 85/ 3 @6%

B @ R. 85/

S 3 F @ R. 90/

A 3 : R : 850.06*0.25= R. 86.28

D R. 90/

P = 90 86.28 =. 3.72

D F / F 16

. 40/ 6

. 38/.

8% . ()

6 , ?

S0= 40/ ; = 8% ; T = 6/12 = 0.50 ; F0=R.35/

T F P (FT0)=S0T

=400.08*0.5= R. 41.63 > R. 38/

A CC::

B 6 F @ R. 38/

S S @ R. 40/ I R 40/ 6 @ 8%

A 6 :

R : 400.08*0.5= R. 41.63

B R 38/ .

P = 41.63 38 =. 3.63


9/26

BGDF (201315) 12

Dr. Pankaj Varshney

D F / F 17

C R.700/ R. 30/ 3

. T 3 I (3)

5% 6 (6) 6%. F

6 .

A, 6 R. 705/.

D F / F 18

A :

:

) B R. 700/ (R 29.60 3 @ 5% &

R. 670.40 6 @ 6% )

) B R. 700/.

) S 6 F @

R.705/


10/26

BGDF (201315) 12

Dr. Pankaj Varshney

D F / F 19

A 3 :

T

R 30/

R 29.60 3 @ 5%

. (29.60 0.05*3/12 = 30)

A 6 :

T :

) R (R 705/)

,

) R R 670.40 I(670.40*(0.06*0.5) = 670.40*1.03045) = R. 690.80

D F / F 20

T 6 :

: . 705/ : .690.80

B ,

.14.20 .. (705 690.80).

N, 6 F (F0) R.

680/ ( R. 705/).

T :

) S R. 700/.

) I : R 29.60 3 @ 5% &

R 670.40 6 @ 6%;

) B 6 F @ R. 680/


11/26

BGDF (201315) 12

Dr. Pankaj Varshney

D F / F 21

A 3 :

T R 29.60 @ 5% (. 29.60 0.05*3/12 = 30),

.

A 6 :T:

) R R. 670.40

(670.40*(0.06*0.5) = 670.40*1.03045 = R.690.80).

) P @ R. 680/,

F .

T 6 :

: . 690.80/ : .680/ B ,

R.10.80 (690.80 680).

D F / F 22

T, F NOT

R.690.80,

.

T, NO ARBITRAGE , F

P R. 690.80.

F (F0) = (0 )

. (= *.)

I = 30 (0.05*3/12) = 29.60

F0= (70029.60) 0.06*6/12 = 670.40 * 1.03045

= . 690.80


12/26

BGDF (201315) 12

Dr. Pankaj Varshney

D F / F 23

A 1 2 5 .

. 50/

6%. 6

?

S0= 50/ ; = 6% ; T= 6/12 ; D2= R 1; D5= R 1

F (F0) = (0 )

I = D21+ D5

2 =10.06*2/12 + 10.06*5/12

= 0.9900 + 0.9753 = 1.9653F0= (50 1.9653)

0.06*6/12 = 48.0347*1.0305

= .49.4976 = . 49.50

D F / F 24

A $4 2 .

$ 99.75. 2 5%

3 6% ( ).

. 3

$ 97, ?

S0 = $ 99.75 ; 2 = 5% ; 3 = 6% T = 3/12 ; C2 = $4.

F (F0) = (0 )

I = C21 = 40.05*2/12 = 4(0.9917) =3.9668

F0

= (99.75 3.9668)0.06*3/12 = 95.7832*1.0151= $ 97.23 > $97

A CC

B 3 @ $97

S @ $ 99.75

I 3.9668 2 @ 5% & $95.7832 3 @ 6%

A 2 : NCF =0; A 3 : 97.2308 97 = $0.2308


13/26

BGDF (201315) 12

Dr. Pankaj Varshney

D F / F 25

.

A D

. C

:

) B , T

,

) S F

.

H @ , T T

T.

D F / F 26

O M ( T), F0. I

ST., F0.

E

, :

F0 T = S0

T

F0= S0 T/T

F0= 0 ()

I F0

>S0

() T,

F0< S0() T,

.


14/26

BGDF (201315) 12

Dr. Pankaj Varshney

D F / F 27

T, S() T

,

.

T, NO ARBITRAGE , F

S ()T.

F (F0) = 0()

D F / F 28

CN N 5100

3.5% . T

8.5% . 6

F I?

S0= 5100 ; = 8.5% ; =3.5%; T= 6 .

F (F0) = S0 ()T

F0= 5100 (0.0850.035)*6/12 = 5100*1.0253

= 5229.10710 = 5229


15/26

BGDF (201315) 12

Dr. Pankaj Varshney

D F / F 29

: C 6 2%

6 . T

10% . T R. 25/

S0= 25 ; = 10% ; T= 6 = 0.5 ;

= 2% 6 = 4% .

= 3.96% .

F (F0) = S0 ()T

F0= 25

(0.10 0.0396)*6/12

= 25*1.03066 = . 25.76652= . 25.77

D F / F 30

F C

() F

?

O , F .

A ,

,

.

FC M = FC FC= F*0 F0

FC = (F*0 F0) = (F*

0 F0)*


16/26

BGDF (201315) 12

Dr. Pankaj Varshney

D F / F 31

F C

C ABC R. 114/. T 7% . A , R.

109. 6

?

S0= 114/ ; S1= 109/; = 7% ; T= 6 .

F P (F0) = S0 T

A = 0 : F0 = 114 (0.07)*6/12 = 114*1.03562 = 118/

A = 1 : F*0= 109 (0.07)*5/12 = 109*1.02960 = 112/

F C M= F*0 F0 = 112118= 6

F C = (F*

0 F0)= 6 (0.07)*5/12 = 6(0.97125)

= 5.83

D F / F 32

F C

A

R. 24/. T

6 . T

10% , R 25/.

?

F0 = 24/; S*

0= 25/ ; = 10% ; T= 6 .

F P N F*0 = S*0 T

A = 0 : F0 = 24/

A = 1 : F*0= 25 (0.10)*6/12 = 25*1.05127 = 26.28 F C M= F*0 F0 = 26.28 24

F C = (F*0 F0) = 2.28(0.10)*6/12

= 2.28(0.9512)

=. 2.17


17/26

BGDF (201315) 12

Dr. Pankaj Varshney

D F / F 33

F C

2 US 2

$ 1.61 . A ,

$ 1.585 . S

6%, ?

F0 = $1.61 ; FN= $1.585 ; = 6% ; T= 1 .

F C M= F*0 F0 = 1.585 1.61

F C = (F*0 F0) = 0.025(0.06)*1/12

= 0.025(0.9952) = $ 0.024875/

I

2,000,000*0.024875 = $49,750/ .

D F / F 34

,

.

H, , F

F .

.

I F , /

, ( )

A , .

H, .

F . F


18/26

BGDF (201315) 12

Dr. Pankaj Varshney

D F / F 35

S, / ,

.

T .

A F ( F

)

.

L F

.

F

, /

F . F

D F / F 36

.

I F , /

, (

)

A , .

H, .

S, / ,

. T .

A F ( F

)

.

F . F


19/26

BGDF (201315) 12

Dr. Pankaj Varshney

D F / F 37

L F

.

F

, /

.

F

F (

) .

F . F

D F / F 38

U .

P (S F ) HC FC.

F/F C

100 FC

=0

100FCF0

HC =T

100FCT

FC =T

100S0

HC =0

1000

HC

HC =T

100FCTF0= 100S0

HCT

F0= 0(

HC

FC)

C FC HC @

0 & HC @ HC FC @ FC& C

FC HC @ F0


20/26

BGDF (201315) 12

Dr. Pankaj Varshney

D F / F 39

2 S I 3% &6% (). S S R. 33.778.

2 S ?

F/F C

S0 = 33.778; HC= 6% ; FC= 3%; T = 2/12

F0= 0(

HC

FC)

= 33.778 (0.06 0.03)2/12

= 33.778 0.005 = 33.778 (1.00501) = . 33.9473

D F / F 40

C ( ).

S, F (F0) = (0+ )

.

F / F C


21/26

BGDF (201315) 12

Dr. Pankaj Varshney

D F / F 41

S0 = R. 18000/ ; = 10% T = 9/12

U = 175 + 1750.10*3/12 +1750.10*6/12 = R. 512.15

F0 = (0+ )

= (18000 +512.15) 0.10*9/12

=18512.15(1.07788) = 19953.95 = . 19,954/ .

F / C

T R. 18000/ . I R.175/ (

). 9 ,

10%..?

D F / F 42

I % C ,

F (F0) = 0( + )

F C

T R. 18000/ . I 3%

. 6 ,

10%..?

S0= R. 18000/ ; = 10%; =3%; T = 6/12

F0 = 0( + )

= (18000) (0.10 + 0.03)*6/12

=18000(1.06716) = . 19,208.86 .


22/26

BGDF (201315) 12

Dr. Pankaj Varshney

D F / F 43

S, F0

> (0+ )

A :

B (S0+ U) @ T .

B .

S .

R T : F0 (0+ )

M , F0 = (0+ )

A C

D F / F 44

N , F0 < (0+ )

A :

S ,

T .

T .

R T : (0+ )

F0

H,

.

I/

.

A C


23/26

BGDF (201315) 12

Dr. Pankaj Varshney

D F / F 45

U

.

O

.

S C

() : F0 = (0+ )

F0 = (0+ ) ( )

F0 = (0)

( + )

A C

D F / F 46

A C

T , , R. 5,500/

. I 4% . I 6

R. 5,800/ ,

,

10%..?

S0= R. 5,500/; F0= R. 5,800/ ; = 10%; =4%;

T = 6/12 F0 = 0( + )

5800 = (5500) (0.10 + 0.04 )*6/12

(1.05455) = (0.10 + 0.04 )*0.5

0.05311 = 0.07 0.5

= 0.03378 = 3.38 %


24/26

BGDF (201315) 12

Dr. Pankaj Varshney

D F / F 47

I

F F . ..

.

FA= S0T, FA .

A

0

F1 =

T S

ln

A

0

F1 = +

T S

ln

D F / F 48

S0= R.25/ ; FA= R 26/; T = 3/12 .

N: S & ,

C F: =0 : +25 = 3/12: 26.: B .

.

C ABC L

. I

R. 25/ 3

R. 26/ ?

A

0

F1 1 26 = =4(0.03922)=0.15688=15.69%

T S 1/4 25

=

ln ln


25/26

BGDF (201315) 12

Dr. Pankaj Varshney

D F / F 49

A, .

C F: =0 : 25 = 3/12: +26.: L

.

()

.

D F / F 50

S

.

I ,

.

I ,

< , @

( & ) @ .

I , > ,

(

& ) @ @ .

S < < .

A


26/26

BGDF (201315) 12

D F / F 51

S0= 1400; FA= 1425; T = 3/12 ; = 8%.

A

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3 Forward Prices-Determination